Study of the intergrain interaction potential and associated instability of dust-lattice plasma oscillations in the presence of ion flow

A comprehensive study of the Debye-Huckel repulsive and ion wakefield induced attractive potentials around a dust grain is presented, including ion flow. It is found that the modified interaction potential (especially the attractive wakefield force) can cause instability of linear dust oscillations propagating in a dusty plasma crystal composed of dust grains in a horizontal arrangement suspended in the sheath region near a conducting wall (electrode). The dependence of dust lattice modes on the ion flow is studied, revealing instability of dust lattice modes for certain values of the ion flow speed. (C) 2003 Elsevier B.V. All rights reserved.

Electron-acoustic plasma waves: Oblique modulation and envelope solitons

Theoretical and numerical studies are presented of the amplitude modulation of electron-acoustic waves (EAWs) propagating in space plasmas whose constituents are inertial cold electrons, Boltzmann distributed hot electrons, and stationary ions. Perturbations oblique to the carrier EAW propagation direction have been considered. The stability analysis, based on a nonlinear Schrodinger equation, reveals that the EAW may become unstable; the stability criteria depend on the angle theta between the modulation and propagation directions. Different types of localized EA excitations are shown to exist.

Nonlinear modulation of transverse dust lattice waves in complex plasma crystals

The occurrence of the modulational instability in transverse dust lattice waves propagating in a one-dimensional dusty plasma crystal is investigated. The amplitude modulation mechanism, which is related to the intrinsic nonlinearity of the sheath electric field, is shown to destabilize the carrier wave under certain conditions, possibly leading to the formation of localized envelope excitations. Explicit expressions for the instability growth rate and threshold are presented and discussed. (C) 2004 American Institute of Physics.

Weakly nonlinear vertical dust grain oscillations in dusty plasma crystals in the presence of a magnetic field

The weakly nonlinear regime of transverse paramagnetic dust grain oscillations in dusty (complex) plasma crystals is discussed. The nonlinearity, which is related to the sheath electric/magnetic field(s) and to the intergrain (electrostatic/magnetic dipole) interactions, is shown to lead to the generation of phase harmonics and, in the case of propagating transverse dust-lattice modes, to the modulational instability of the carrier wave due to self-interaction. The stability profile depends explicitly on the form of the electric and magnetic fields in the plasma sheath. The long term evolution of the modulated wave packet, which is described by a nonlinear Schrodinger-type equation, may lead to propagating localized envelope structures whose exact forms are presented and discussed. Explicit suggestions for experimental investigations are put forward. (C) 2004 American Institute of Physics.

Modulated wave packets and envelope solitary structures in complex plasmas

A theoretical study is presented of the nonlinear amplitude modulation of waves propagating in unmagnetized plasmas contaminated by charged dust particles. Distinct well-known dusty plasma modes are explicitly considered, namely, the dust-acoustic wave, the dust-ion acoustic wave, and transverse dust-lattice waves. Using a multiple-scale technique, a nonlinear Schrodinger-type equation is derived, describing the evolution of the wave amplitude. A stability analysis reveals the possibility for modulational instability to occur, possibly leading to the formation of different types of envelope-localized excitations (solitary waves), under conditions which depend on the wave dispersion laws and intrinsic dusty plasma parameters.

Complete nonlinear theory of longitudinal-to-transverse dust lattice mode coupling in a single-layer dusty plasma crystal

A comprehensive nonlinear model is put forward for coupled longitudinal to transverse displacements in a horizontal dust mono-layer, levitated under the combined influence of gravity and an electric and/or magnetic sheath field. A set of coupled nonlinear evolution equations are obtained in a discrete description, and a pair of coupled (Boussinesq-like) PDEs are obtained in the continuum approximation. Finally, the amplitude modulation of the coupled modes is discussed, pointing out the importance of the coupling. All these results are generic, i.e. valid for any assumed form of the inter-grain interaction potential U and the sheath potential Phi.

Stability of dust lattice modes in the presence of charged dust grain polarization in plasmas

We discuss the effect of the attractive force associated with overlapping Debye spheres on the dispersion properties of the longitudinal and transverse dust lattice waves in strongly coupled dust crystals. The dust grain attraction is shown to contribute to a destabilization of the longitudinal dust lattice oscillations. The (optic-like) transverse mode dispersion law is shown to change. due to the Debye sphere dressing effect, from the known inverse-dispersive ("backward wave") form into a normal dispersive law (i.e. the group velocity changes sign). The stability of one-dimensionless bi-layers, consisting of (alternating) negatively and positively charged dust particles, is also discussed. The range of parameter values (mainly in terms of the lattice parameter kappa) where the above predictions are valid, are presented. (c) 2005 Elsevier B.V. All rights reserved.

Dust lattice wave dispersion relations in two-dimensional hexagonal crystals including the effect of dust charge polarization

A dusty plasma crystalline configuration with equal charge dust grains and mass is considered. Both charge and mass of each dust species are taken to be constant. Two differential equations for a two-dimensional hexagonal crystal on the basis of a Yukawa-type potential energy and a

Discrete solitons and vortices in hexagonal and honeycomb lattices: Existence, stability, and dynamics

We consider a prototypical dynamical lattice model, namely, the discrete nonlinear Schrodinger equation on nonsquare lattice geometries. We present a systematic classification of the solutions that arise in principal six-lattice-site and three-lattice-site contours in the form of both discrete multipole solitons and discrete vortices. Additionally to identifying the possible states, we analytically track their linear stability both qualitatively and quantitatively. We find that among the six-site configurations, the

Fokker-Planck equation for a test-particle weakly coupled to a magnetized plasma

We consider the derivation of a kinetic equation for a charged test particle weakly interacting with an electrostatic plasma in thermal equilibrium, subject to a uniform external magnetic field. The Liouville equation leads to a generalized master equation to second order in the `weak' interaction; a Fokker-Planck-type equation then follows as a `Markovian' approximation. It is shown that such an equation does not preserve the positivity of the distribution function f(x,v;t). By applying techniques developed in the theory of open systems, a correct Fokker-Planck equation is derived. Explicit expressions for the diffusion and drift coefficients, depending on the magnetic field, are obtained.

A comparison of nonstaggered compact FDTD schemes for the 3D wave equation

This paper aims at providing a better insight into the 3D approximations of the wave equation using compact finite-difference time-domain (FDTD) schemes in the context of room acoustic simulations. A general family of 3D compact explicit and implicit schemes based on a nonstaggered rectilinear grid is analyzed in terms of stability, numerical error, and accuracy. Various special cases are compared and the most accurate explicit and implicit schemes are identified. Further considerations presented in the paper include the direct relationship with other numerical approaches found in the literature on room acoustic modeling such as the 3D digital waveguide mesh and Yee's staggered grid technique.

Probing magnetic order in ultracold lattice gases

A forthcoming challenge in ultracold lattice gases is the simulation of quantum magnetism. That involves both the preparation of the lattice atomic gas in the desired spin state and the probing of the state. Here we demonstrate how a probing scheme based on atom-light interfaces gives access to the order parameters of nontrivial quantum magnetic phases, allowing us to characterize univocally strongly correlated magnetic systems produced in ultracold gases. This method, which is also nondemolishing, yields spatially resolved spin correlations and can be applied to bosons or fermions. As a proof of principle, we apply this method to detect the complete phase diagram displayed by a chain of (rotationally invariant) spin-1 bosons.

Berry phase in open quantum systems: a quantum Langevin equation approach

The evolution of a two level system with a slowly varying Hamiltonian, modeled as a spin 1/2 in a slowly varying magnetic field, and interacting with a quantum environment, modeled as a bath of harmonic oscillators is analyzed using a quantum Langevin approach. This allows to easily obtain the dissipation time and the correction to the Berry phase in the case of an adiabatic cyclic evolution.